Ramblings of a post-denominational frummer yid. Comments to benchorin613@yahoo.com

Wednesday, December 28, 2005

On the first night of Chanukah, Yisrael Aumann delivered his Nobel Lecture in Hebrew University. He discussed, in popular terms, some consequences of the ideas for which he won the prize.

Imagine two players playing a game in which either can choose to cooperate or act selfishly. If both cooperate, they each get 3000. If both act selfishly, they each get 1000. If one cooperates and the other acts selfishly, the selfish one gets 4000 and the cooperative one gets 0. Note that for each player (A), regardless of what the other player (B) does, A makes 1000 more by acting selfishly than by cooperating. For that reason, the only "equilibrium point" of the game is the one in which both act selfishly. The result is that both end up with 1000 rather than 3000. Obviously, this is not optimal for either one. (Formally, we say that this result is not "Pareto optimal", i.e., there are solutions in which both players can do better.) If the players could negotiate an agreement and trust that such an agreement would be enforced (say, by a third party), then they obviously could do better.

Now let's imagine that there is no third party enforcer but rather the same players are doomed to play the same game over and over again. It turns out that in this scenario, cooperative behavior is self-reinforcing, since a player is prevented from acting selfishly by the threat that the other player will react to selfish behavior by acting selfishly himself in subsequent games. Thus, in repeated games, players will ultimately cooperate even without an enforcer.

There is, however, one limitation to this self-reinforcement. Players must value profits in the future almost as much as profits now. If they don't, the threat of future losses as punishment for short-term profits is an inadequate threat. Aumann repeated at least three times that the practical consequence of this is that those who place too high a premium on "peace now" will delay peace indefinitely, while those who establish a credible threat of retaliation have a chance to achieve peace sooner.

After the lecture, there was a reception for friends, family, colleagues and a variety of bessere mentschen. A classical cellist played while hors d'ouevres were served; bekitzur, the organizers were aiming for a somewhat hoity toity atmosphere. Except that Aumann insisted on first getting together a minyan for maariv, then lighting chanukah lecht and then singing Maoz Tzur -- all six stanzas until the bitter end. Gevaldig.